Realtime multiGNSS singlefrequency precise point positioning
Abstract
Precise Point Positioning (PPP) is a popular Global Positioning System (GPS) processing strategy, thanks to its high precision without requiring additional GPS infrastructure. SingleFrequency PPP (SFPPP) takes this one step further by no longer relying on expensive dualfrequency GPS receivers, while maintaining a relatively high positioning accuracy. The use of GPSonly SFPPP for lane identification and mapping on a motorway has previously been demonstrated successfully. However, the performance was shown to depend strongly on the number of available satellites, limiting the application of SFPPP to relatively open areas. We investigate whether the applicability can be extended by moving from using only GPS to using multiple Global Navigation Satellite Systems (GNSS). Next to GPS, the Russian GLONASS system is at present the only fully functional GNSS and was selected for this reason. We introduce our approach to multiGNSS SFPPP and demonstrate its performance by means of several experiments. Results show that multiGNSS SFPPP indeed outperforms GPSonly SFPPP in particular in case of reduced sky visibility.
Keywords
Single frequency Precise point positioning MultiGNSS GPS GLONASS Low cost Lane identification AutomotiveIntroduction
Precise Point Positioning (PPP) is a popular Global Positioning System (GPS) processing strategy, thanks to its high precision without requiring additional GPS infrastructure (Zumberge et al. 1997). SingleFrequency PPP (SFPPP) takes this one step further by no longer relying on expensive dualfrequency GPS receivers, while maintaining a relatively high positioning accuracy (Le and Tiberius 2007; Choy 2009; Shi et al. 2012). In fact, SFPPP can be considered the most accurate realtime Global Navigation Satellite System (GNSS) processing strategy that is possible with a lowcost GNSS receiver and without any further requirements on other sensors or supporting GNSS infrastructure. Several different approaches exist to correct for the ionospheric delays in SFPPP, each with its own performance characteristics. First, the ionosphere can be eliminated from the observations by forming an ionosphericfree combination of the code and phase measurements (Yunck 1993; Choy 2009), but this leads to a long convergence period before a sufficient accuracy is obtained. Second, the ionospheric delay can be parameterized and estimated together with the other unknown parameters, while constraining the ionospheric delay, which reduces the convergence period to some extent (Shi et al. 2012). Finally, the ionosphere can be corrected using sufficiently accurate external ionospheric data without estimating any additional ionospheric parameters (Le and Tiberius 2007). The latter approach almost completely eliminates the convergence period, while keeping a reasonable accuracy, and was demonstrated for the realtime automotive application of lanelevel positioning in the motorway, under operational conditions (van Bree et al. 2011; Knoop et al. 2016).
However, the performance was shown to depend strongly on the number of available satellites (de Bakker and Tiberius 2016), limiting the application of SFPPP to relatively open areas. One way of increasing the number of satellites is by moving from using only GPS to using multiple GNSS simultaneously (Angrisano et al. 2013; Cai et al. 2013; Lou et al. 2016). In this publication, we investigate whether the applicability of realtime SFPPP with a lowcost receiver for lane identification can be extended to more challenging areas by using multiple GNSS. Several other GNSS might be considered such as the Chinese Beidou or European Galileo system. However, we focus on the Russian GLONASS system, since it is at present the only fully functional GNSS besides GPS. We introduce our approach to multiGNSS SFPPP and demonstrate its performance by means of several experiments. Results show that multiGNSS SFPPP indeed outperforms GPSonly SFPPP in particular in case of reduced sky visibility.
SFPPP model and corrections

The precise satellite position coordinates in vector r ^{ s }, the satellite clock offset t ^{ s } and the relativistic effect υ. The GPS satellite positions and clock offsets are computed from Keplerian elements (ISGPS200D 2004). The GLONASS satellite positions and clock offsets are computed through numerical integration with a fourthorder Runge–Kutta method (GLONASSICD 2008). The satellite positions and clock offsets for both systems are then corrected with the IGS realtime service correction stream collected via Ntrip (Caissy et al. 2012).

The (neutral) tropospheric delay n. The tropospheric delay is modeled with the a priori Saastamoinen model (Saastamoinen 1972) using the Ifadis mapping function (Ifadis 1986) and parameters from the 1976 US Standard Atmosphere (Stull 1995).

The ionospheric delay i and satellite differential code bias d ^{ s }. The ionospheric delay is computed a priori using the 1day predicted Global Ionosphere Maps (GIM) from the Center for Orbit Determination in Europe (CODE) together with the corresponding differential code biases (Schaer 1999).

The carrier phase observations are corrected for the phase windup at the receiver φ _{ r } and satellite φ ^{ s } (Wu et al. 1993). The user orientation is derived from position differences over time.
Note that besides the satellite differential code biases and the receiver GPS–GLONASS intersystem bias, no explicit hardware delays are present in the model. This is because they cannot be estimated separately. The pseudorange hardware delays are absorbed by the clock offsets both at the receiver (in the estimated receiver clock) and at the satellites (in the precise satellite clocks). The receiver and satellite carrier phase hardware delays are assumed constant and are absorbed by the estimated ambiguities. This is only allowed because the ambiguities are estimated as “floating” realvalued parameters (i.e., they are not fixed to integer values).
Stochastic model
Observations from different epochs are assumed to be uncorrelated, and consequently, the ambiguity estimates from previous epochs are uncorrelated with the current observations. Observations to different satellites are also assumed to be uncorrelated, which means that Q _{ pp }, Q _{ ϕϕ }, and Q _{ pϕ } are diagonal matrices.
Standard deviation σ in meters for each of the variance components in the stochastic model
GPS  GLONASS  Satellite  Atmosphere  

Code  Phase  Code  Phase  Orbit  Clock  Troposphere  Ionosphere 
σ _{ p }  σ _{ ϕ }  σ _{ p }  σ _{ ϕ }  \(\sigma_{{r^{s} }}^{{}}\)  \(\sigma_{{t^{s} }}^{{}}\)  σ _{ n }  σ _{ i } 
0.5  0.005  1.5  0.0075  0.025  0.030  0.07  0.2 
Measurement noise
As shown this reduces the variance of the resulting estimator by 10% (the standard deviation reduces about 5%), not a huge improvement over the single observation. Hence, we can expect that, in cases where GPSonly SFPPP is already performing well, the advantage of adding GLONASS will be rather limited.
However, there are a number of factors that are not considered in this simple example. Firstly, we only looked at the raw pseudorange measurement noise. The complete stochastic model also involves the carrier phase, the PPP corrections, correlations, and especially for the carrier phase measurements, this will bring the GPS and GLONASS precisions closer together (although the GLONASS corrections can also be expected to be of somewhat lower quality than the GPS corrections). Secondly, the observation model, i.e., the direct observation of the unknown parameter, is very favorable for estimation. In practice, the number of satellites might be low, or the geometry might be unfavorable for position estimation. In those cases the addition of GLONASS satellites might be much more significant. On the other hand, Fig. 4 shows that on average the number of available GLONASS satellites is lower than the number of available GPS satellites, which again reduces the GLONASS contribution. Finally, the example only involves a single epoch of data. If more epochs are considered, the (GLONASS) measurement noise might even out, and GLONASS could contribute to reducing position biases over longer time periods.
Dynamic model
In our default positioning filter, the carrier phase ambiguities are the only parameters propagated from a previous epoch to the current epoch. The receiver position coordinates, the receiver clock offset, and the intersystem bias are estimated each epoch anew—there is no vehicle dynamics model involved. In the following, we will call this the kinematic model.
However, to assess the impact of the time update on the performance, we will also consider two alternative models. First is a static model in which the receiver coordinates are also assumed constant and propagated from a previous epoch to the current epoch. This is the strongest possible position dynamics model, since it adds no uncertainty over time, and can thus provide a lower bound on the resulting position uncertainty. And second is a singleepoch model in which neither the ambiguities nor the position coordinates are propagated, and all unknown parameters are computed from a single epoch of data. With this model, the carrier phase measurements do not contribute to the position estimation, making it essentially a pseudorangeonly model. It illustrates a hypothetical situation in which the tracking to each satellite is interrupted between each two epochs, and it provides an upper bound to the position uncertainty.
Integrity monitoring
In parallel with the positioning filter, statistical hypothesis testing is used to detect errors in the observations and propagated ambiguities (e.g., caused by excessive multipath or a cycle slip), based on the DIA procedure (Detection, Identification and Adaptation; Teunissen 1990). If one of the pseudorange measurements is identified, it is removed from the model. If either a carrier phase measurement or ambiguity is identified, the ambiguity for that satellite is reset (i.e., the propagated ambiguity is removed).
Shadowing and multipath
Realtime singleconstellation (GPS) SFPPP was previously shown to provide submeter accuracy with short initialization time with a lowend receiver and antenna (Knoop et al. 2016). However, obstruction of the line of sight from the receiver to the satellites (called shadowing) can significantly reduce the number of available satellites in builtup areas and degrade their relative geometry for positioning.
Additionally, reflected signals arriving at the receiver, called multipath, may bias the measurement and consequently the computed position. Integrity monitoring relies on redundancy in the model and is thus weakened if the number of available satellites is reduced, exacerbating the problem.
Therefore, while GPS SFPPP works well for lane identification and lane mapping on motorways in open areas, it may not work on belowgrade open cut motorways, motorways which pass through highrise areas or motorways with tall roadside noise barriers. We will try to extend the SFPPP applicability to these types of motorways, by incorporating a second GNSS (GLONASS). This will increase the number of available satellites and might improve the geometry sufficiently to retain the required position accuracy.
Experiments and results
Results from two experiments conducted with a ublox M8T EVK receiver and supplied antenna are presented. The first experiment involves a stationary receiver on top of the Netherlands Measurement institute (NMi) building in Delft, and the second experiment was conducted with a vehicle driving over the A15, part of the orbital motorway around Rotterdam, in the Netherlands.
The receiver was connected to a raspberry pi 3 or laptop, logging the raw measurements. Precise orbit and clock corrections from the IGS realtime service were collected simultaneously in the office, using the BNC Ntrip client software, and corresponding merged broadcast ephemeris files for GPS and GLONASS were downloaded from the IGS. Predicted ionosphere maps and satellite differential code biases, from CODE, were downloaded prior to the experiment. The positions were then estimated with our multiGNSS SFPPP implementation simulating realtime operation, i.e., strictly using data available at the time of measurement only.
Stationary experiment
The positioning performance is assessed by comparing the computed position to the accurate reference position using the following performance metrics: mean, standard deviation (std), rootmeansquare (rms) error and the 95th percentile (95%).
The bottom three panels of Fig. 5 present the position errors in the north, east and up directions over the first 200 epochs. For the results in these panels only, all parameters are reset after each 200 epochs, and the filter is restarted. The thin lines represent the 57 individual runs; the thick line shows, at each epoch, the rms over all runs. The computed positions start to converge to the true position as the carrier phase measurements start to contribute more and more to the solution, but the improvement is not very large and gets smaller over time. The top panel already illustrated that the errors do not go to zero, even after 4 days. This is most likely due to nonzero mean errors due to multipath, hardware delays and residual atmosphere delays.
Positioning performance of the stationary experiment (elevation mask 5°), after the positioning filter has converged for 100 epochs
Single epoch  Kinematic  Static  

Mean  std  rms  95%  Mean  std  rms  95%  Mean  std  rms  95%  
G  
N  0.06  0.50  0.50  0.95  −0.06  0.34  0.34  0.70  −0.04  0.28  0.28  0.52 
E  −0.10  0.49  0.50  0.96  −0.08  0.42  0.42  0.89  −0.10  0.42  0.43  0.83 
U  1.05  1.04  1.47  2.73  0.81  0.71  1.07  2.20  0.72  0.48  0.86  1.51 
R  
N  0.16  2.39  2.39  4.88  −0.15  1.17  1.18  2.48  −0.06  0.84  0.83  1.38 
E  −0.09  2.29  2.28  4.56  −0.05  1.98  1.97  3.99  −0.09  1.38  1.38  2.51 
U  1.20  5.32  5.43  10.57  0.87  2.96  3.08  6.25  0.63  1.31  1.44  2.73 
M  
N  0.05  0.51  0.51  1.03  −0.06  0.33  0.33  0.66  −0.05  0.30  0.30  0.62 
E  −0.10  0.49  0.49  0.99  −0.06  0.41  0.41  0.79  −0.09  0.38  0.39  0.72 
U  1.06  1.10  1.52  2.93  0.77  0.79  1.10  2.22  0.70  0.55  0.89  1.55 
Under more difficult conditions, and especially also for the motorway experiments, letting the filter converge for 50 min is not very realistic, as the available satellites will change much more quickly, restarting the ambiguity estimation for these satellites each time. Therefore, in the following, we will simply compute the performance metrics over the complete time series, without resetting the filter, for the kinematic model, while only providing fully converged results for the static model. The expected performance of the singleepoch model should not depend on the time that the filter has run at all, although it can vary with, e.g., the number of available satellites. For the stationary data, we present both methods of computing the performance metrics here side by side for comparison.
Positioning performance of the stationary experiment (elevation mask 5°), computed over all epochs, disregarding filter convergence, and final position errors of static processing after 4 days
Single epoch  Kinematic  Static  

Mean  std  rms  95%  Mean  std  rms  95%  
G  
N  0.09  0.51  0.52  0.99  −0.20  0.26  0.33  0.64  −0.11 
E  −0.11  0.48  0.49  0.96  0.01  0.40  0.40  0.83  0.02 
U  1.06  1.01  1.47  2.78  0.46  0.49  0.68  1.29  0.38 
R  
N  0.13  2.35  2.36  4.68  −0.01  0.97  0.97  1.91  −0.10 
E  −0.17  2.29  2.30  4.47  0.16  1.26  1.27  2.53  0.05 
U  1.35  5.21  5.38  10.89  0.30  1.94  1.96  4.06  0.42 
M  
N  0.09  0.55  0.56  1.11  −0.11  0.34  0.36  0.70  −0.11 
E  −0.11  0.47  0.49  0.95  0.08  0.35  0.35  0.69  0.04 
U  1.06  1.10  1.53  2.97  0.37  0.73  0.82  1.58  0.42 
Stationary experiment with reduced sky visibility
Positioning performance of the stationary receiver (elevation mask 30°), computed over all epochs, disregarding filter convergence, and final position errors of static processing after 4 days. GPSonly values represent 93.7% of epochs; GLONASSonly values represent 71.5% of epochs; and no solution could be computed at the other epochs
Single epoch  Kinematic  Static  

Mean  std  rms  95%  Mean  std  rms  95%  
G  
N  −0.73  86.68  86.68  3.09  −0.75  70.45  70.45  1.45  −0.12 
E  −0.55  31.88  31.88  1.84  −0.45  25.90  25.90  1.56  0.08 
U  −1.33  183.6  183.6  6.00  −1.19  149.5  149.5  3.78  0.29 
R  
N  −3.22  152.6  152.6  79.81  −2.54  125.7  125.7  62.29  −0.04 
E  −2.74  100.7  100.7  50.91  0.98  90.64  90.64  60.04  0.22 
U  16.81  380.9  381.3  273.5  6.45  322.0  322.1  199.9  0.43 
M  
N  0.16  1.38  1.39  2.90  −0.11  0.48  0.49  1.04  −0.12 
E  −0.12  0.78  0.79  1.60  −0.07  0.53  0.53  1.02  0.03 
U  0.94  2.83  2.98  6.38  0.30  1.10  1.14  2.28  0.24 
Automotive experiment: A15 orbital motorway
Figure 11 shows the skyplot a few minutes into the A15 experiment. The obstruction caused by the noise barrier is shown with the hatched area in cyan. The barrier does not stop all signals (at times satellites with lower elevation were observed), but does strongly reduce satellite reception from the southern direction.
Conclusions
The results show that GPS + GLONASS multiGNSS SFPPP performs well under all circumstances considered in this research. This includes kinematic processing in a reference stationlike setup with free view of the sky above 5° elevation and processing with an (imposed) 30° elevation cutoff angle as well as processing of data collected on a motorway chosen specifically for its reduced sky visibility. The noise barrier along the A15 motorway did not prevent lanelevel positioning (i.e., accuracy better than 1.75 m) with the SFPPP method.
Comparisons between GPSonly and GPS + GLONASS results show that the GLONASS addition has a marginal impact in those cases where GPSonly already performs well. This is in line with expectations, given the lower precision of the GLONASS signals with respect to the GPS signals. The longterm mean position coordinates do show some improvement due to the GLONASS addition. However, under more challenging conditions, the differences are striking. The multiGNSS solution is much more resistant to reduced visibility and keeps performing well even with a 30° cutoff angle (98.7% availability). While the GPSonly performance breaks down, availability of lanelevel accuracy decreases considerably. Similarly, lanelevel accurate positioning remained possible 83.7% of the time, on the A15 motorway with a tall roadside noise barrier, even if additional signal obstruction was simulated. GLONASSonly processing performs as expected, but does not provide lanelevel accuracy.
Notes
Acknowledgements
This research was performed, in close cooperation with the Department of Transport and Planning, as part of the “Taking the Fast Lane” project funded by the STW Technology Foundation of the Netherlands Organization for Scientific Research Grant STWOTP 13771.
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